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You can assume that lines that appear straight are, in fact, straight lines. Ditto for segments and rays.

You can assume that the parts of the diagram are connected as shown and in the order shown. For example, if points A, B and C appear on a line in that order, then they are collinear and B is actually between A and B.

You can assume that segments and angles explicitly marked as congruent are, in fact, congruent.

You can assume that angles marked as right angles are, in fact, right angles; and that lines marked as parallel (with the same number of arrowheads) are parallel.

Pretty much anything else is off limits. In particular:

Angles that look congruent aren't, unless marked so.

Segments that look congruent aren't, unless marked so.

A length or angle that appears larger than another may not be.

Lines that appear parallel or perpendicular aren't, unless marked so.

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If you are talking about proofs, then the rules are simpler:

For formal proofs, you assume nothing that isn't an axiom, a postulate, or a previously proved statement (proposition, theorem, lemma, etc.)